keen-botkit/docs/assets/lib/d3/d3.js

Bot Kit Integration for Keen IO

// https://d3js.org Version 4.4.1. Copyright 2017 Mike Bostock.
(function (global, factory) {
  typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
  typeof define === 'function' && define.amd ? define(['exports'], factory) :
  (factory((global.d3 = global.d3 || {})));
}(this, (function (exports) { 'use strict';

var version = "4.4.1";

var ascending = function(a, b) {
  return a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN;
};

var bisector = function(compare) {
  if (compare.length === 1) compare = ascendingComparator(compare);
  return {
    left: function(a, x, lo, hi) {
      if (lo == null) lo = 0;
      if (hi == null) hi = a.length;
      while (lo < hi) {
        var mid = lo + hi >>> 1;
        if (compare(a[mid], x) < 0) lo = mid + 1;
        else hi = mid;
      }
      return lo;
    },
    right: function(a, x, lo, hi) {
      if (lo == null) lo = 0;
      if (hi == null) hi = a.length;
      while (lo < hi) {
        var mid = lo + hi >>> 1;
        if (compare(a[mid], x) > 0) hi = mid;
        else lo = mid + 1;
      }
      return lo;
    }
  };
};

function ascendingComparator(f) {
  return function(d, x) {
    return ascending(f(d), x);
  };
}

var ascendingBisect = bisector(ascending);
var bisectRight = ascendingBisect.right;
var bisectLeft = ascendingBisect.left;

var descending = function(a, b) {
  return b < a ? -1 : b > a ? 1 : b >= a ? 0 : NaN;
};

var number = function(x) {
  return x === null ? NaN : +x;
};

var variance = function(array, f) {
  var n = array.length,
      m = 0,
      a,
      d,
      s = 0,
      i = -1,
      j = 0;

  if (f == null) {
    while (++i < n) {
      if (!isNaN(a = number(array[i]))) {
        d = a - m;
        m += d / ++j;
        s += d * (a - m);
      }
    }
  }

  else {
    while (++i < n) {
      if (!isNaN(a = number(f(array[i], i, array)))) {
        d = a - m;
        m += d / ++j;
        s += d * (a - m);
      }
    }
  }

  if (j > 1) return s / (j - 1);
};

var deviation = function(array, f) {
  var v = variance(array, f);
  return v ? Math.sqrt(v) : v;
};

var extent = function(array, f) {
  var i = -1,
      n = array.length,
      a,
      b,
      c;

  if (f == null) {
    while (++i < n) if ((b = array[i]) != null && b >= b) { a = c = b; break; }
    while (++i < n) if ((b = array[i]) != null) {
      if (a > b) a = b;
      if (c < b) c = b;
    }
  }

  else {
    while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = c = b; break; }
    while (++i < n) if ((b = f(array[i], i, array)) != null) {
      if (a > b) a = b;
      if (c < b) c = b;
    }
  }

  return [a, c];
};

var array = Array.prototype;

var slice = array.slice;
var map = array.map;

var constant = function(x) {
  return function() {
    return x;
  };
};

var identity = function(x) {
  return x;
};

var range = function(start, stop, step) {
  start = +start, stop = +stop, step = (n = arguments.length) < 2 ? (stop = start, start = 0, 1) : n < 3 ? 1 : +step;

  var i = -1,
      n = Math.max(0, Math.ceil((stop - start) / step)) | 0,
      range = new Array(n);

  while (++i < n) {
    range[i] = start + i * step;
  }

  return range;
};

var e10 = Math.sqrt(50);
var e5 = Math.sqrt(10);
var e2 = Math.sqrt(2);

var ticks = function(start, stop, count) {
  var step = tickStep(start, stop, count);
  return range(
    Math.ceil(start / step) * step,
    Math.floor(stop / step) * step + step / 2, // inclusive
    step
  );
};

function tickStep(start, stop, count) {
  var step0 = Math.abs(stop - start) / Math.max(0, count),
      step1 = Math.pow(10, Math.floor(Math.log(step0) / Math.LN10)),
      error = step0 / step1;
  if (error >= e10) step1 *= 10;
  else if (error >= e5) step1 *= 5;
  else if (error >= e2) step1 *= 2;
  return stop < start ? -step1 : step1;
}

var sturges = function(values) {
  return Math.ceil(Math.log(values.length) / Math.LN2) + 1;
};

var histogram = function() {
  var value = identity,
      domain = extent,
      threshold = sturges;

  function histogram(data) {
    var i,
        n = data.length,
        x,
        values = new Array(n);

    for (i = 0; i < n; ++i) {
      values[i] = value(data[i], i, data);
    }

    var xz = domain(values),
        x0 = xz[0],
        x1 = xz[1],
        tz = threshold(values, x0, x1);

    // Convert number of thresholds into uniform thresholds.
    if (!Array.isArray(tz)) tz = ticks(x0, x1, tz);

    // Remove any thresholds outside the domain.
    var m = tz.length;
    while (tz[0] <= x0) tz.shift(), --m;
    while (tz[m - 1] >= x1) tz.pop(), --m;

    var bins = new Array(m + 1),
        bin;

    // Initialize bins.
    for (i = 0; i <= m; ++i) {
      bin = bins[i] = [];
      bin.x0 = i > 0 ? tz[i - 1] : x0;
      bin.x1 = i < m ? tz[i] : x1;
    }

    // Assign data to bins by value, ignoring any outside the domain.
    for (i = 0; i < n; ++i) {
      x = values[i];
      if (x0 <= x && x <= x1) {
        bins[bisectRight(tz, x, 0, m)].push(data[i]);
      }
    }

    return bins;
  }

  histogram.value = function(_) {
    return arguments.length ? (value = typeof _ === "function" ? _ : constant(_), histogram) : value;
  };

  histogram.domain = function(_) {
    return arguments.length ? (domain = typeof _ === "function" ? _ : constant([_[0], _[1]]), histogram) : domain;
  };

  histogram.thresholds = function(_) {
    return arguments.length ? (threshold = typeof _ === "function" ? _ : Array.isArray(_) ? constant(slice.call(_)) : constant(_), histogram) : threshold;
  };

  return histogram;
};

var threshold = function(array, p, f) {
  if (f == null) f = number;
  if (!(n = array.length)) return;
  if ((p = +p) <= 0 || n < 2) return +f(array[0], 0, array);
  if (p >= 1) return +f(array[n - 1], n - 1, array);
  var n,
      h = (n - 1) * p,
      i = Math.floor(h),
      a = +f(array[i], i, array),
      b = +f(array[i + 1], i + 1, array);
  return a + (b - a) * (h - i);
};

var freedmanDiaconis = function(values, min, max) {
  values = map.call(values, number).sort(ascending);
  return Math.ceil((max - min) / (2 * (threshold(values, 0.75) - threshold(values, 0.25)) * Math.pow(values.length, -1 / 3)));
};

var scott = function(values, min, max) {
  return Math.ceil((max - min) / (3.5 * deviation(values) * Math.pow(values.length, -1 / 3)));
};

var max = function(array, f) {
  var i = -1,
      n = array.length,
      a,
      b;

  if (f == null) {
    while (++i < n) if ((b = array[i]) != null && b >= b) { a = b; break; }
    while (++i < n) if ((b = array[i]) != null && b > a) a = b;
  }

  else {
    while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = b; break; }
    while (++i < n) if ((b = f(array[i], i, array)) != null && b > a) a = b;
  }

  return a;
};

var mean = function(array, f) {
  var s = 0,
      n = array.length,
      a,
      i = -1,
      j = n;

  if (f == null) {
    while (++i < n) if (!isNaN(a = number(array[i]))) s += a; else --j;
  }

  else {
    while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) s += a; else --j;
  }

  if (j) return s / j;
};

var median = function(array, f) {
  var numbers = [],
      n = array.length,
      a,
      i = -1;

  if (f == null) {
    while (++i < n) if (!isNaN(a = number(array[i]))) numbers.push(a);
  }

  else {
    while (++i < n) if (!isNaN(a = number(f(array[i], i, array)))) numbers.push(a);
  }

  return threshold(numbers.sort(ascending), 0.5);
};

var merge = function(arrays) {
  var n = arrays.length,
      m,
      i = -1,
      j = 0,
      merged,
      array;

  while (++i < n) j += arrays[i].length;
  merged = new Array(j);

  while (--n >= 0) {
    array = arrays[n];
    m = array.length;
    while (--m >= 0) {
      merged[--j] = array[m];
    }
  }

  return merged;
};

var min = function(array, f) {
  var i = -1,
      n = array.length,
      a,
      b;

  if (f == null) {
    while (++i < n) if ((b = array[i]) != null && b >= b) { a = b; break; }
    while (++i < n) if ((b = array[i]) != null && a > b) a = b;
  }

  else {
    while (++i < n) if ((b = f(array[i], i, array)) != null && b >= b) { a = b; break; }
    while (++i < n) if ((b = f(array[i], i, array)) != null && a > b) a = b;
  }

  return a;
};

var pairs = function(array) {
  var i = 0, n = array.length - 1, p = array[0], pairs = new Array(n < 0 ? 0 : n);
  while (i < n) pairs[i] = [p, p = array[++i]];
  return pairs;
};

var permute = function(array, indexes) {
  var i = indexes.length, permutes = new Array(i);
  while (i--) permutes[i] = array[indexes[i]];
  return permutes;
};

var scan = function(array, compare) {
  if (!(n = array.length)) return;
  var i = 0,
      n,
      j = 0,
      xi,
      xj = array[j];

  if (!compare) compare = ascending;

  while (++i < n) if (compare(xi = array[i], xj) < 0 || compare(xj, xj) !== 0) xj = xi, j = i;

  if (compare(xj, xj) === 0) return j;
};

var shuffle = function(array, i0, i1) {
  var m = (i1 == null ? array.length : i1) - (i0 = i0 == null ? 0 : +i0),
      t,
      i;

  while (m) {
    i = Math.random() * m-- | 0;
    t = array[m + i0];
    array[m + i0] = array[i + i0];
    array[i + i0] = t;
  }

  return array;
};

var sum = function(array, f) {
  var s = 0,
      n = array.length,
      a,
      i = -1;

  if (f == null) {
    while (++i < n) if (a = +array[i]) s += a; // Note: zero and null are equivalent.
  }

  else {
    while (++i < n) if (a = +f(array[i], i, array)) s += a;
  }

  return s;
};

var transpose = function(matrix) {
  if (!(n = matrix.length)) return [];
  for (var i = -1, m = min(matrix, length), transpose = new Array(m); ++i < m;) {
    for (var j = -1, n, row = transpose[i] = new Array(n); ++j < n;) {
      row[j] = matrix[j][i];
    }
  }
  return transpose;
};

function length(d) {
  return d.length;
}

var zip = function() {
  return transpose(arguments);
};

var prefix = "$";

function Map() {}

Map.prototype = map$1.prototype = {
  constructor: Map,
  has: function(key) {
    return (prefix + key) in this;
  },
  get: function(key) {
    return this[prefix + key];
  },
  set: function(key, value) {
    this[prefix + key] = value;
    return this;
  },
  remove: function(key) {
    var property = prefix + key;
    return property in this && delete this[property];
  },
  clear: function() {
    for (var property in this) if (property[0] === prefix) delete this[property];
  },
  keys: function() {
    var keys = [];
    for (var property in this) if (property[0] === prefix) keys.push(property.slice(1));
    return keys;
  },
  values: function() {
    var values = [];
    for (var property in this) if (property[0] === prefix) values.push(this[property]);
    return values;
  },
  entries: function() {
    var entries = [];
    for (var property in this) if (property[0] === prefix) entries.push({key: property.slice(1), value: this[property]});
    return entries;
  },
  size: function() {
    var size = 0;
    for (var property in this) if (property[0] === prefix) ++size;
    return size;
  },
  empty: function() {
    for (var property in this) if (property[0] === prefix) return false;
    return true;
  },
  each: function(f) {
    for (var property in this) if (property[0] === prefix) f(this[property], property.slice(1), this);
  }
};

function map$1(object, f) {
  var map = new Map;

  // Copy constructor.
  if (object instanceof Map) object.each(function(value, key) { map.set(key, value); });

  // Index array by numeric index or specified key function.
  else if (Array.isArray(object)) {
    var i = -1,
        n = object.length,
        o;

    if (f == null) while (++i < n) map.set(i, object[i]);
    else while (++i < n) map.set(f(o = object[i], i, object), o);
  }

  // Convert object to map.
  else if (object) for (var key in object) map.set(key, object[key]);

  return map;
}

var nest = function() {
  var keys = [],
      sortKeys = [],
      sortValues,
      rollup,
      nest;

  function apply(array, depth, createResult, setResult) {
    if (depth >= keys.length) return rollup != null
        ? rollup(array) : (sortValues != null
        ? array.sort(sortValues)
        : array);

    var i = -1,
        n = array.length,
        key = keys[depth++],
        keyValue,
        value,
        valuesByKey = map$1(),
        values,
        result = createResult();

    while (++i < n) {
      if (values = valuesByKey.get(keyValue = key(value = array[i]) + "")) {
        values.push(value);
      } else {
        valuesByKey.set(keyValue, [value]);
      }
    }

    valuesByKey.each(function(values, key) {
      setResult(result, key, apply(values, depth, createResult, setResult));
    });

    return result;
  }

  function entries(map, depth) {
    if (++depth > keys.length) return map;
    var array, sortKey = sortKeys[depth - 1];
    if (rollup != null && depth >= keys.length) array = map.entries();
    else array = [], map.each(function(v, k) { array.push({key: k, values: entries(v, depth)}); });
    return sortKey != null ? array.sort(function(a, b) { return sortKey(a.key, b.key); }) : array;
  }

  return nest = {
    object: function(array) { return apply(array, 0, createObject, setObject); },
    map: function(array) { return apply(array, 0, createMap, setMap); },
    entries: function(array) { return entries(apply(array, 0, createMap, setMap), 0); },
    key: function(d) { keys.push(d); return nest; },
    sortKeys: function(order) { sortKeys[keys.length - 1] = order; return nest; },
    sortValues: function(order) { sortValues = order; return nest; },
    rollup: function(f) { rollup = f; return nest; }
  };
};

function createObject() {
  return {};
}

function setObject(object, key, value) {
  object[key] = value;
}

function createMap() {
  return map$1();
}

function setMap(map, key, value) {
  map.set(key, value);
}

function Set() {}

var proto = map$1.prototype;

Set.prototype = set.prototype = {
  constructor: Set,
  has: proto.has,
  add: function(value) {
    value += "";
    this[prefix + value] = value;
    return this;
  },
  remove: proto.remove,
  clear: proto.clear,
  values: proto.keys,
  size: proto.size,
  empty: proto.empty,
  each: proto.each
};

function set(object, f) {
  var set = new Set;

  // Copy constructor.
  if (object instanceof Set) object.each(function(value) { set.add(value); });

  // Otherwise, assume it’s an array.
  else if (object) {
    var i = -1, n = object.length;
    if (f == null) while (++i < n) set.add(object[i]);
    else while (++i < n) set.add(f(object[i], i, object));
  }

  return set;
}

var keys = function(map) {
  var keys = [];
  for (var key in map) keys.push(key);
  return keys;
};

var values = function(map) {
  var values = [];
  for (var key in map) values.push(map[key]);
  return values;
};

var entries = function(map) {
  var entries = [];
  for (var key in map) entries.push({key: key, value: map[key]});
  return entries;
};

var uniform = function(min, max) {
  min = min == null ? 0 : +min;
  max = max == null ? 1 : +max;
  if (arguments.length === 1) max = min, min = 0;
  else max -= min;
  return function() {
    return Math.random() * max + min;
  };
};

var normal = function(mu, sigma) {
  var x, r;
  mu = mu == null ? 0 : +mu;
  sigma = sigma == null ? 1 : +sigma;
  return function() {
    var y;

    // If available, use the second previously-generated uniform random.
    if (x != null) y = x, x = null;

    // Otherwise, generate a new x and y.
    else do {
      x = Math.random() * 2 - 1;
      y = Math.random() * 2 - 1;
      r = x * x + y * y;
    } while (!r || r > 1);

    return mu + sigma * y * Math.sqrt(-2 * Math.log(r) / r);
  };
};

var logNormal = function() {
  var randomNormal = normal.apply(this, arguments);
  return function() {
    return Math.exp(randomNormal());
  };
};

var irwinHall = function(n) {
  return function() {
    for (var sum = 0, i = 0; i < n; ++i) sum += Math.random();
    return sum;
  };
};

var bates = function(n) {
  var randomIrwinHall = irwinHall(n);
  return function() {
    return randomIrwinHall() / n;
  };
};

var exponential = function(lambda) {
  return function() {
    return -Math.log(1 - Math.random()) / lambda;
  };
};

function linear(t) {
  return +t;
}

function quadIn(t) {
  return t * t;
}

function quadOut(t) {
  return t * (2 - t);
}

function quadInOut(t) {
  return ((t *= 2) <= 1 ? t * t : --t * (2 - t) + 1) / 2;
}

function cubicIn(t) {
  return t * t * t;
}

function cubicOut(t) {
  return --t * t * t + 1;
}

function cubicInOut(t) {
  return ((t *= 2) <= 1 ? t * t * t : (t -= 2) * t * t + 2) / 2;
}

var exponent = 3;

var polyIn = (function custom(e) {
  e = +e;

  function polyIn(t) {
    return Math.pow(t, e);
  }

  polyIn.exponent = custom;

  return polyIn;
})(exponent);

var polyOut = (function custom(e) {
  e = +e;

  function polyOut(t) {
    return 1 - Math.pow(1 - t, e);
  }

  polyOut.exponent = custom;

  return polyOut;
})(exponent);

var polyInOut = (function custom(e) {
  e = +e;

  function polyInOut(t) {
    return ((t *= 2) <= 1 ? Math.pow(t, e) : 2 - Math.pow(2 - t, e)) / 2;
  }

  polyInOut.exponent = custom;

  return polyInOut;
})(exponent);

var pi = Math.PI;
var halfPi = pi / 2;

function sinIn(t) {
  return 1 - Math.cos(t * halfPi);
}

function sinOut(t) {
  return Math.sin(t * halfPi);
}

function sinInOut(t) {
  return (1 - Math.cos(pi * t)) / 2;
}

function expIn(t) {
  return Math.pow(2, 10 * t - 10);
}

function expOut(t) {
  return 1 - Math.pow(2, -10 * t);
}

function expInOut(t) {
  return ((t *= 2) <= 1 ? Math.pow(2, 10 * t - 10) : 2 - Math.pow(2, 10 - 10 * t)) / 2;
}

function circleIn(t) {
  return 1 - Math.sqrt(1 - t * t);
}

function circleOut(t) {
  return Math.sqrt(1 - --t * t);
}

function circleInOut(t) {
  return ((t *= 2) <= 1 ? 1 - Math.sqrt(1 - t * t) : Math.sqrt(1 - (t -= 2) * t) + 1) / 2;
}

var b1 = 4 / 11;
var b2 = 6 / 11;
var b3 = 8 / 11;
var b4 = 3 / 4;
var b5 = 9 / 11;
var b6 = 10 / 11;
var b7 = 15 / 16;
var b8 = 21 / 22;
var b9 = 63 / 64;
var b0 = 1 / b1 / b1;

function bounceIn(t) {
  return 1 - bounceOut(1 - t);
}

function bounceOut(t) {
  return (t = +t) < b1 ? b0 * t * t : t < b3 ? b0 * (t -= b2) * t + b4 : t < b6 ? b0 * (t -= b5) * t + b7 : b0 * (t -= b8) * t + b9;
}

function bounceInOut(t) {
  return ((t *= 2) <= 1 ? 1 - bounceOut(1 - t) : bounceOut(t - 1) + 1) / 2;
}

var overshoot = 1.70158;

var backIn = (function custom(s) {
  s = +s;

  function backIn(t) {
    return t * t * ((s + 1) * t - s);
  }

  backIn.overshoot = custom;

  return backIn;
})(overshoot);

var backOut = (function custom(s) {
  s = +s;

  function backOut(t) {
    return --t * t * ((s + 1) * t + s) + 1;
  }

  backOut.overshoot = custom;

  return backOut;
})(overshoot);

var backInOut = (function custom(s) {
  s = +s;

  function backInOut(t) {
    return ((t *= 2) < 1 ? t * t * ((s + 1) * t - s) : (t -= 2) * t * ((s + 1) * t + s) + 2) / 2;
  }

  backInOut.overshoot = custom;

  return backInOut;
})(overshoot);

var tau = 2 * Math.PI;
var amplitude = 1;
var period = 0.3;

var elasticIn = (function custom(a, p) {
  var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

  function elasticIn(t) {
    return a * Math.pow(2, 10 * --t) * Math.sin((s - t) / p);
  }

  elasticIn.amplitude = function(a) { return custom(a, p * tau); };
  elasticIn.period = function(p) { return custom(a, p); };

  return elasticIn;
})(amplitude, period);

var elasticOut = (function custom(a, p) {
  var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

  function elasticOut(t) {
    return 1 - a * Math.pow(2, -10 * (t = +t)) * Math.sin((t + s) / p);
  }

  elasticOut.amplitude = function(a) { return custom(a, p * tau); };
  elasticOut.period = function(p) { return custom(a, p); };

  return elasticOut;
})(amplitude, period);

var elasticInOut = (function custom(a, p) {
  var s = Math.asin(1 / (a = Math.max(1, a))) * (p /= tau);

  function elasticInOut(t) {
    return ((t = t * 2 - 1) < 0
        ? a * Math.pow(2, 10 * t) * Math.sin((s - t) / p)
        : 2 - a * Math.pow(2, -10 * t) * Math.sin((s + t) / p)) / 2;
  }

  elasticInOut.amplitude = function(a) { return custom(a, p * tau); };
  elasticInOut.period = function(p) { return custom(a, p); };

  return elasticInOut;
})(amplitude, period);

var area = function(polygon) {
  var i = -1,
      n = polygon.length,
      a,
      b = polygon[n - 1],
      area = 0;

  while (++i < n) {
    a = b;
    b = polygon[i];
    area += a[1] * b[0] - a[0] * b[1];
  }

  return area / 2;
};

var centroid = function(polygon) {
  var i = -1,
      n = polygon.length,
      x = 0,
      y = 0,
      a,
      b = polygon[n - 1],
      c,
      k = 0;

  while (++i < n) {
    a = b;
    b = polygon[i];
    k += c = a[0] * b[1] - b[0] * a[1];
    x += (a[0] + b[0]) * c;
    y += (a[1] + b[1]) * c;
  }

  return k *= 3, [x / k, y / k];
};

// Returns the 2D cross product of AB and AC vectors, i.e., the z-component of
// the 3D cross product in a quadrant I Cartesian coordinate system (+x is
// right, +y is up). Returns a positive value if ABC is counter-clockwise,
// negative if clockwise, and zero if the points are collinear.
var cross = function(a, b, c) {
  return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
};

function lexicographicOrder(a, b) {
  return a[0] - b[0] || a[1] - b[1];
}

// Computes the upper convex hull per the monotone chain algorithm.
// Assumes points.length >= 3, is sorted by x, unique in y.
// Returns an array of indices into points in left-to-right order.
function computeUpperHullIndexes(points) {
  var n = points.length,
      indexes = [0, 1],
      size = 2;

  for (var i = 2; i < n; ++i) {
    while (size > 1 && cross(points[indexes[size - 2]], points[indexes[size - 1]], points[i]) <= 0) --size;
    indexes[size++] = i;
  }

  return indexes.slice(0, size); // remove popped points
}

var hull = function(points) {
  if ((n = points.length) < 3) return null;

  var i,
      n,
      sortedPoints = new Array(n),
      flippedPoints = new Array(n);

  for (i = 0; i < n; ++i) sortedPoints[i] = [+points[i][0], +points[i][1], i];
  sortedPoints.sort(lexicographicOrder);
  for (i = 0; i < n; ++i) flippedPoints[i] = [sortedPoints[i][0], -sortedPoints[i][1]];

  var upperIndexes = computeUpperHullIndexes(sortedPoints),
      lowerIndexes = computeUpperHullIndexes(flippedPoints);

  // Construct the hull polygon, removing possible duplicate endpoints.
  var skipLeft = lowerIndexes[0] === upperIndexes[0],
      skipRight = lowerIndexes[lowerIndexes.length - 1] === upperIndexes[upperIndexes.length - 1],
      hull = [];

  // Add upper hull in right-to-l order.
  // Then add lower hull in left-to-right order.
  for (i = upperIndexes.length - 1; i >= 0; --i) hull.push(points[sortedPoints[upperIndexes[i]][2]]);
  for (i = +skipLeft; i < lowerIndexes.length - skipRight; ++i) hull.push(points[sortedPoints[lowerIndexes[i]][2]]);

  return hull;
};

var contains = function(polygon, point) {
  var n = polygon.length,
      p = polygon[n - 1],
      x = point[0], y = point[1],
      x0 = p[0], y0 = p[1],
      x1, y1,
      inside = false;

  for (var i = 0; i < n; ++i) {
    p = polygon[i], x1 = p[0], y1 = p[1];
    if (((y1 > y) !== (y0 > y)) && (x < (x0 - x1) * (y - y1) / (y0 - y1) + x1)) inside = !inside;
    x0 = x1, y0 = y1;
  }

  return inside;
};

var length$1 = function(polygon) {
  var i = -1,
      n = polygon.length,
      b = polygon[n - 1],
      xa,
      ya,
      xb = b[0],
      yb = b[1],
      perimeter = 0;

  while (++i < n) {
    xa = xb;
    ya = yb;
    b = polygon[i];
    xb = b[0];
    yb = b[1];
    xa -= xb;
    ya -= yb;
    perimeter += Math.sqrt(xa * xa + ya * ya);
  }

  return perimeter;
};

var pi$1 = Math.PI;
var tau$1 = 2 * pi$1;
var epsilon = 1e-6;
var tauEpsilon = tau$1 - epsilon;

function Path() {
  this._x0 = this._y0 = // start of current subpath
  this._x1 = this._y1 = null; // end of current subpath
  this._ = "";
}

function path() {
  return new Path;
}

Path.prototype = path.prototype = {
  constructor: Path,
  moveTo: function(x, y) {
    this._ += "M" + (this._x0 = this._x1 = +x) + "," + (this._y0 = this._y1 = +y);
  },
  closePath: function() {
    if (this._x1 !== null) {
      this._x1 = this._x0, this._y1 = this._y0;
      this._ += "Z";
    }
  },
  lineTo: function(x, y) {
    this._ += "L" + (this._x1 = +x) + "," + (this._y1 = +y);
  },
  quadraticCurveTo: function(x1, y1, x, y) {
    this._ += "Q" + (+x1) + "," + (+y1) + "," + (this._x1 = +x) + "," + (this._y1 = +y);
  },
  bezierCurveTo: function(x1, y1, x2, y2, x, y) {
    this._ += "C" + (+x1) + "," + (+y1) + "," + (+x2) + "," + (+y2) + "," + (this._x1 = +x) + "," + (this._y1 = +y);
  },
  arcTo: function(x1, y1, x2, y2, r) {
    x1 = +x1, y1 = +y1, x2 = +x2, y2 = +y2, r = +r;
    var x0 = this._x1,
        y0 = this._y1,
        x21 = x2 - x1,
        y21 = y2 - y1,
        x01 = x0 - x1,
        y01 = y0 - y1,
        l01_2 = x01 * x01 + y01 * y01;

    // Is the radius negative? Error.
    if (r < 0) throw new Error("negative radius: " + r);

    // Is this path empty? Move to (x1,y1).
    if (this._x1 === null) {
      this._ += "M" + (this._x1 = x1) + "," + (this._y1 = y1);
    }

    // Or, is (x1,y1) coincident with (x0,y0)? Do nothing.
    else if (!(l01_2 > epsilon)) {}

    // Or, are (x0,y0), (x1,y1) and (x2,y2) collinear?
    // Equivalently, is (x1,y1) coincident with (x2,y2)?
    // Or, is the radius zero? Line to (x1,y1).
    else if (!(Math.abs(y01 * x21 - y21 * x01) > epsilon) || !r) {
      this._ += "L" + (this._x1 = x1) + "," + (this._y1 = y1);
    }

    // Otherwise, draw an arc!
    else {
      var x20 = x2 - x0,
          y20 = y2 - y0,
          l21_2 = x21 * x21 + y21 * y21,
          l20_2 = x20 * x20 + y20 * y20,
          l21 = Math.sqrt(l21_2),
          l01 = Math.sqrt(l01_2),
          l = r * Math.tan((pi$1 - Math.acos((l21_2 + l01_2 - l20_2) / (2 * l21 * l01))) / 2),
          t01 = l / l01,
          t21 = l / l21;

      // If the start tangent is not coincident with (x0,y0), line to.
      if (Math.abs(t01 - 1) > epsilon) {
        this._ += "L" + (x1 + t01 * x01) + "," + (y1 + t01 * y01);
      }

      this._ += "A" + r + "," + r + ",0,0," + (+(y01 * x20 > x01 * y20)) + "," + (this._x1 = x1 + t21 * x21) + "," + (this._y1 = y1 + t21 * y21);
    }
  },
  arc: function(x, y, r, a0, a1, ccw) {
    x = +x, y = +y, r = +r;
    var dx = r * Math.cos(a0),
        dy = r * Math.sin(a0),
        x0 = x + dx,
        y0 = y + dy,
        cw = 1 ^ ccw,
        da = ccw ? a0 - a1 : a1 - a0;

    // Is the radius negative? Error.
    if (r < 0) throw new Error("negative radius: " + r);

    // Is this path empty? Move to (x0,y0).
    if (this._x1 === null) {
      this._ += "M" + x0 + "," + y0;
    }

    // Or, is (x0,y0) not coincident with the previous point? Line to (x0,y0).
    else if (Math.abs(this._x1 - x0) > epsilon || Math.abs(this._y1 - y0) > epsilon) {
      this._ += "L" + x0 + "," + y0;
    }

    // Is this arc empty? We’re done.
    if (!r) return;

    // Is this a complete circle? Draw two arcs to complete the circle.
    if (da > tauEpsilon) {
      this._ += "A" + r + "," + r + ",0,1," + cw + "," + (x - dx) + "," + (y - dy) + "A" + r + "," + r + ",0,1," + cw + "," + (this._x1 = x0) + "," + (this._y1 = y0);
    }

    // Otherwise, draw an arc!
    else {
      if (da < 0) da = da % tau$1 + tau$1;
      this._ += "A" + r + "," + r + ",0," + (+(da >= pi$1)) + "," + cw + "," + (this._x1 = x + r * Math.cos(a1)) + "," + (this._y1 = y + r * Math.sin(a1));
    }
  },
  rect: function(x, y, w, h) {
    this._ += "M" + (this._x0 = this._x1 = +x) + "," + (this._y0 = this._y1 = +y) + "h" + (+w) + "v" + (+h) + "h" + (-w) + "Z";
  },
  toString: function() {
    return this._;
  }
};

var tree_add = function(d) {
  var x = +this._x.call(null, d),
      y = +this._y.call(null, d);
  return add(this.cover(x, y), x, y, d);
};

function add(tree, x, y, d) {
  if (isNaN(x) || isNaN(y)) return tree; // ignore invalid points

  var parent,
      node = tree._root,
      leaf = {data: d},
      x0 = tree._x0,
      y0 = tree._y0,
      x1 = tree._x1,
      y1 = tree._y1,
      xm,
      ym,
      xp,
      yp,
      right,
      bottom,
      i,
      j;

  // If the tree is empty, initialize the root as a leaf.
  if (!node) return tree._root = leaf, tree;

  // Find the existing leaf for the new point, or add it.
  while (node.length) {
    if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
    if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
    if (parent = node, !(node = node[i = bottom << 1 | right])) return parent[i] = leaf, tree;
  }

  // Is the new point is exactly coincident with the existing point?
  xp = +tree._x.call(null, node.data);
  yp = +tree._y.call(null, node.data);
  if (x === xp && y === yp) return leaf.next = node, parent ? parent[i] = leaf : tree._root = leaf, tree;

  // Otherwise, split the leaf node until the old and new point are separated.
  do {
    parent = parent ? parent[i] = new Array(4) : tree._root = new Array(4);
    if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
    if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
  } while ((i = bottom << 1 | right) === (j = (yp >= ym) << 1 | (xp >= xm)));
  return parent[j] = node, parent[i] = leaf, tree;
}

function addAll(data) {
  var d, i, n = data.length,
      x,
      y,
      xz = new Array(n),
      yz = new Array(n),
      x0 = Infinity,
      y0 = Infinity,
      x1 = -Infinity,
      y1 = -Infinity;

  // Compute the points and their extent.
  for (i = 0; i < n; ++i) {
    if (isNaN(x = +this._x.call(null, d = data[i])) || isNaN(y = +this._y.call(null, d))) continue;
    xz[i] = x;
    yz[i] = y;
    if (x < x0) x0 = x;
    if (x > x1) x1 = x;
    if (y < y0) y0 = y;
    if (y > y1) y1 = y;
  }

  // If there were no (valid) points, inherit the existing extent.
  if (x1 < x0) x0 = this._x0, x1 = this._x1;
  if (y1 < y0) y0 = this._y0, y1 = this._y1;

  // Expand the tree to cover the new points.
  this.cover(x0, y0).cover(x1, y1);

  // Add the new points.
  for (i = 0; i < n; ++i) {
    add(this, xz[i], yz[i], data[i]);
  }

  return this;
}

var tree_cover = function(x, y) {
  if (isNaN(x = +x) || isNaN(y = +y)) return this; // ignore invalid points

  var x0 = this._x0,
      y0 = this._y0,
      x1 = this._x1,
      y1 = this._y1;

  // If the quadtree has no extent, initialize them.
  // Integer extent are necessary so that if we later double the extent,
  // the existing quadrant boundaries don’t change due to floating point error!
  if (isNaN(x0)) {
    x1 = (x0 = Math.floor(x)) + 1;
    y1 = (y0 = Math.floor(y)) + 1;
  }

  // Otherwise, double repeatedly to cover.
  else if (x0 > x || x > x1 || y0 > y || y > y1) {
    var z = x1 - x0,
        node = this._root,
        parent,
        i;

    switch (i = (y < (y0 + y1) / 2) << 1 | (x < (x0 + x1) / 2)) {
      case 0: {
        do parent = new Array(4), parent[i] = node, node = parent;
        while (z *= 2, x1 = x0 + z, y1 = y0 + z, x > x1 || y > y1);
        break;
      }
      case 1: {
        do parent = new Array(4), parent[i] = node, node = parent;
        while (z *= 2, x0 = x1 - z, y1 = y0 + z, x0 > x || y > y1);
        break;
      }
      case 2: {
        do parent = new Array(4), parent[i] = node, node = parent;
        while (z *= 2, x1 = x0 + z, y0 = y1 - z, x > x1 || y0 > y);
        break;
      }
      case 3: {
        do parent = new Array(4), parent[i] = node, node = parent;
        while (z *= 2, x0 = x1 - z, y0 = y1 - z, x0 > x || y0 > y);
        break;
      }
    }

    if (this._root && this._root.length) this._root = node;
  }

  // If the quadtree covers the point already, just return.
  else return this;

  this._x0 = x0;
  this._y0 = y0;
  this._x1 = x1;
  this._y1 = y1;
  return this;
};

var tree_data = function() {
  var data = [];
  this.visit(function(node) {
    if (!node.length) do data.push(node.data); while (node = node.next)
  });
  return data;
};

var tree_extent = function(_) {
  return arguments.length
      ? this.cover(+_[0][0], +_[0][1]).cover(+_[1][0], +_[1][1])
      : isNaN(this._x0) ? undefined : [[this._x0, this._y0], [this._x1, this._y1]];
};

var Quad = function(node, x0, y0, x1, y1) {
  this.node = node;
  this.x0 = x0;
  this.y0 = y0;
  this.x1 = x1;
  this.y1 = y1;
};

var tree_find = function(x, y, radius) {
  var data,
      x0 = this._x0,
      y0 = this._y0,
      x1,
      y1,
      x2,
      y2,
      x3 = this._x1,
      y3 = this._y1,
      quads = [],
      node = this._root,
      q,
      i;

  if (node) quads.push(new Quad(node, x0, y0, x3, y3));
  if (radius == null) radius = Infinity;
  else {
    x0 = x - radius, y0 = y - radius;
    x3 = x + radius, y3 = y + radius;
    radius *= radius;
  }

  while (q = quads.pop()) {

    // Stop searching if this quadrant can’t contain a closer node.
    if (!(node = q.node)
        || (x1 = q.x0) > x3
        || (y1 = q.y0) > y3
        || (x2 = q.x1) < x0
        || (y2 = q.y1) < y0) continue;

    // Bisect the current quadrant.
    if (node.length) {
      var xm = (x1 + x2) / 2,
          ym = (y1 + y2) / 2;

      quads.push(
        new Quad(node[3], xm, ym, x2, y2),
        new Quad(node[2], x1, ym, xm, y2),
        new Quad(node[1], xm, y1, x2, ym),
        new Quad(node[0], x1, y1, xm, ym)
      );

      // Visit the closest quadrant first.
      if (i = (y >= ym) << 1 | (x >= xm)) {
        q = quads[quads.length - 1];
        quads[quads.length - 1] = quads[quads.length - 1 - i];
        quads[quads.length - 1 - i] = q;
      }
    }

    // Visit this point. (Visiting coincident points isn’t necessary!)
    else {
      var dx = x - +this._x.call(null, node.data),
          dy = y - +this._y.call(null, node.data),
          d2 = dx * dx + dy * dy;
      if (d2 < radius) {
        var d = Math.sqrt(radius = d2);
        x0 = x - d, y0 = y - d;
        x3 = x + d, y3 = y + d;
        data = node.data;
      }
    }
  }

  return data;
};

var tree_remove = function(d) {
  if (isNaN(x = +this._x.call(null, d)) || isNaN(y = +this._y.call(null, d))) return this; // ignore invalid points

  var parent,
      node = this._root,
      retainer,
      previous,
      next,
      x0 = this._x0,
      y0 = this._y0,
      x1 = this._x1,
      y1 = this._y1,
      x,
      y,
      xm,
      ym,
      right,
      bottom,
      i,
      j;

  // If the tree is empty, initialize the root as a leaf.
  if (!node) return this;

  // Find the leaf node for the point.
  // While descending, also retain the deepest parent with a non-removed sibling.
  if (node.length) while (true) {
    if (right = x >= (xm = (x0 + x1) / 2)) x0 = xm; else x1 = xm;
    if (bottom = y >= (ym = (y0 + y1) / 2)) y0 = ym; else y1 = ym;
    if (!(parent = node, node = node[i = bottom << 1 | right])) return this;
    if (!node.length) break;
    if (parent[(i + 1) & 3] || parent[(i + 2) & 3] || parent[(i + 3) & 3]) retainer = parent, j = i;
  }

  // Find the point to remove.
  while (node.data !== d) if (!(previous = node, node = node.next)) return this;
  if (next = node.next) delete node.next;

  // If there are multiple coincident points, remove just the point.
  if (previous) return (next ? previous.next = next : delete previous.next), this;

  // If this is the root point, remove it.
  if (!parent) return this._root = next, this;

  // Remove this leaf.
  next ? parent[i] = next : delete parent[i];

  // If the parent now contains exactly one leaf, collapse superfluous parents.
  if ((node = parent[0] || parent[1] || parent[2] || parent[3])
      && node === (parent[3] || parent[2] || parent[1] || parent[0])
      && !node.length) {
    if (retainer) retainer[j] = node;
    else this._root = node;
  }

  return this;
};

function removeAll(data) {
  for (var i = 0, n = data.length; i < n; ++i) this.remove(data[i]);
  return this;
}

var tree_root = function() {
  return this._root;
};

var tree_size = function() {
  var size = 0;
  this.visit(function(node) {
    if (!node.length) do ++size; while (node = node.next)
  });
  return size;
};

var tree_visit = function(callback) {
  var quads = [], q, node = this._root, child, x0, y0, x1, y1;
  if (node) quads.push(new Quad(node, this._x0, this._y0, this._x1, this._y1));
  while (q = quads.pop()) {
    if (!callback(node = q.node, x0 = q.x0, y0 = q.y0, x1 = q.x1, y1 = q.y1) && node.length) {
      var xm = (x0 + x1) / 2, ym = (y0 + y1) / 2;
      if (child = node[3]) quads.push(new Quad(child, xm, ym, x1, y1));
      if (child = node[2]) quads.push(new Quad(child, x0, ym, xm, y1));
      if (child = node[1]) quads.push(new Quad(child, xm, y0, x1, ym));
      if (child = node[0]) quads.push(new Quad(child, x0, y0, xm, ym));
    }
  }
  return this;
};

var tree_visitAfter = function(callback) {
  var quads = [], next = [], q;
  if (this._root) quads.push(new Quad(this._root, this._x0, this._y0, this._x1, this._y1));
  while (q = quads.pop()) {
    var node = q.node;
    if (node.length) {
      var child, x0 = q.x0, y0 = q.y0, x1 = q.x1, y1 = q.y1, xm = (x0 + x1) / 2, ym = (y0 + y1) / 2;
      if (child = node[0]) quads.push(new Quad(child, x0, y0, xm, ym));
      if (child = node[1]) quads.push(new Quad(child, xm, y0, x1, ym));
      if (child = node[2]) quads.push(new Quad(child, x0, ym, xm, y1));
      if (child = node[3]) quads.push(new Quad(child, xm, ym, x1, y1));
    }
    next.push(q);
  }
  while (q = next.pop()) {
    callback(q.node, q.x0, q.y0, q.x1, q.y1);
  }
  return this;
};

function defaultX(d) {
  return d[0];
}

var tree_x = function(_) {
  return arguments.length ? (this._x = _, this) : this._x;
};

function defaultY(d) {
  return d[1];
}

var tree_y = function(_) {
  return arguments.length ? (this._y = _, this) : this._y;
};

function quadtree(nodes, x, y) {
  var tree = new Quadtree(x == null ? defaultX : x, y == null ? defaultY : y, NaN, NaN, NaN, NaN);
  return nodes == null ? tree : tree.addAll(nodes);
}

function Quadtree(x, y, x0, y0, x1, y1) {
  this._x = x;
  this._y = y;
  this._x0 = x0;
  this._y0 = y0;
  this._x1 = x1;
  this._y1 = y1;
  this._root = undefined;
}

function leaf_copy(leaf) {
  var copy = {data: leaf.data}, next = copy;
  while (leaf = leaf.next) next = next.next = {data: leaf.data};
  return copy;
}

var treeProto = quadtree.prototype = Quadtree.prototype;

treeProto.copy = function() {
  var copy = new Quadtree(this._x, this._y, this._x0, this._y0, this._x1, this._y1),
      node = this._root,
      nodes,
      child;

  if (!node) return copy;

  if (!node.length) return copy._root = leaf_copy(node), copy;

  nodes = [{source: node, target: copy._root = new Array(4)}];
  while (node = nodes.pop()) {
    for (var i = 0; i < 4; ++i) {
      if (child = node.source[i]) {
        if (child.length) nodes.push({source: child, target: node.target[i] = new Array(4)});
        else node.target[i] = leaf_copy(child);
      }
    }
  }

  return copy;
};

treeProto.add = tree_add;
treeProto.addAll = addAll;
treeProto.cover = tree_cover;
treeProto.data = tree_data;
treeProto.extent = tree_extent;
treeProto.find = tree_find;
treeProto.remove = tree_remove;
treeProto.removeAll = removeAll;
treeProto.root = tree_root;
treeProto.size = tree_size;
treeProto.visit = tree_visit;
treeProto.visitAfter = tree_visitAfter;
treeProto.x = tree_x;
treeProto.y = tree_y;

var slice$1 = [].slice;

var noabort = {};

function Queue(size) {
  if (!(size >= 1)) throw new Error;
  this._size = size;
  this._call =
  this._error = null;
  this._tasks = [];
  this._data = [];
  this._waiting =
  this._active =
  this._ended =
  this._start = 0; // inside a synchronous task callback?
}

Queue.prototype = queue.prototype = {
  constructor: Queue,
  defer: function(callback) {
    if (typeof callback !== "function" || this._call) throw new Error;
    if (this._error != null) return this;
    var t = slice$1.call(arguments, 1);
    t.push(callback);
    ++this._waiting, this._tasks.push(t);
    poke(this);
    return this;
  },
  abort: function() {
    if (this._error == null) abort(this, new Error("abort"));
    return this;
  },
  await: function(callback) {
    if (typeof callback !== "function" || this._call) throw new Error;
    this._call = function(error, results) { callback.apply(null, [error].concat(results)); };
    maybeNotify(this);
    return this;
  },
  awaitAll: function(callback) {
    if (typeof callback !== "function" || this._call) throw new Error;
    this._call = callback;
    maybeNotify(this);
    return this;
  }
};

function poke(q) {
  if (!q._start) {
    try { start(q); } // let the current task complete
    catch (e) {
      if (q._tasks[q._ended + q._active - 1]) abort(q, e); // task errored synchronously
      else if (!q._data) throw e; // await callback errored synchronously
    }
  }
}

function start(q) {
  while (q._start = q._waiting && q._active < q._size) {
    var i = q._ended + q._active,
        t = q._tasks[i],
        j = t.length - 1,
        c = t[j];
    t[j] = end(q, i);
    --q._waiting, ++q._active;
    t = c.apply(null, t);
    if (!q._tasks[i]) continue; // task finished synchronously
    q._tasks[i] = t || noabort;
  }
}

function end(q, i) {
  return function(e, r) {
    if (!q._tasks[i]) return; // ignore multiple callbacks
    --q._active, ++q._ended;
    q._tasks[i] = null;
    if (q._error != null) return; // ignore secondary errors
    if (e != null) {
      abort(q, e);
    } else {
      q._data[i] = r;
      if (q._waiting) poke(q);
      else maybeNotify(q);
    }
  };
}

function abort(q, e) {
  var i = q._tasks.length, t;
  q._error = e; // ignore active callbacks
  q._data = undefined; // allow gc
  q._waiting = NaN; // prevent starting

  while (--i >= 0) {
    if (t = q._tasks[i]) {
      q._tasks[i] = null;
      if (t.abort) {
        try { t.abort(); }
        catch (e) { /* ignore */ }
      }
    }
  }

  q._active = NaN; // allow notification
  maybeNotify(q);
}

function maybeNotify(q) {
  if (!q._active && q._call) {
    var d = q._data;
    q._data = undefined; // allow gc
    q._call(q._error, d);
  }
}

function queue(concurrency) {
  return new Queue(arguments.length ? +concurrency : Infinity);
}

var constant$1 = function(x) {
  return function constant() {
    return x;
  };
};

var epsilon$1 = 1e-12;
var pi$2 = Math.PI;
var halfPi$1 = pi$2 / 2;
var tau$2 = 2 * pi$2;

function arcInnerRadius(d) {
  return d.innerRadius;
}

function arcOuterRadius(d) {
  return d.outerRadius;
}

function arcStartAngle(d) {
  return d.startAngle;
}

function arcEndAngle(d) {
  return d.endAngle;
}

function arcPadAngle(d) {
  return d && d.padAngle; // Note: optional!
}

function asin(x) {
  return x >= 1 ? halfPi$1 : x <= -1 ? -halfPi$1 : Math.asin(x);
}

function intersect(x0, y0, x1, y1, x2, y2, x3, y3) {
  var x10 = x1 - x0, y10 = y1 - y0,
      x32 = x3 - x2, y32 = y3 - y2,
      t = (x32 * (y0 - y2) - y32 * (x0 - x2)) / (y32 * x10 - x32 * y10);
  return [x0 + t * x10, y0 + t * y10];
}

// Compute perpendicular offset line of length rc.
// http://mathworld.wolfram.com/Circle-LineIntersection.html
function cornerTangents(x0, y0, x1, y1, r1, rc, cw) {
  var x01 = x0 - x1,
      y01 = y0 - y1,
      lo = (cw ? rc : -rc) / Math.sqrt(x01 * x01 + y01 * y01),
      ox = lo * y01,
      oy = -lo * x01,
      x11 = x0 + ox,
      y11 = y0 + oy,
      x10 = x1 + ox,
      y10 = y1 + oy,
      x00 = (x11 + x10) / 2,
      y00 = (y11 + y10) / 2,
      dx = x10 - x11,
      dy = y10 - y11,
      d2 = dx * dx + dy * dy,
      r = r1 - rc,
      D = x11 * y10 - x10 * y11,
      d = (dy < 0 ? -1 : 1) * Math.sqrt(Math.max(0, r * r * d2 - D * D)),
      cx0 = (D * dy - dx * d) / d2,
      cy0 = (-D * dx - dy * d) / d2,
      cx1 = (D * dy + dx * d) / d2,
      cy1 = (-D * dx + dy * d) / d2,
      dx0 = cx0 - x00,
      dy0 = cy0 - y00,
      dx1 = cx1 - x00,
      dy1 = cy1 - y00;

  // Pick the closer of the two intersection points.
  // TODO Is there a faster way to determine which intersection to use?
  if (dx0 * dx0 + dy0 * dy0 > dx1 * dx1 + dy1 * dy1) cx0 = cx1, cy0 = cy1;

  return {
    cx: cx0,
    cy: cy0,
    x01: -ox,
    y01: -oy,
    x11: cx0 * (r1 / r - 1),
    y11: cy0 * (r1 / r - 1)
  };
}

var arc = function() {
  var innerRadius = arcInnerRadius,
      outerRadius = arcOuterRadius,
      cornerRadius = constant$1(0),
      padRadius = null,
      startAngle = arcStartAngle,
      endAngle = arcEndAngle,
      padAngle = arcPadAngle,
      context = null;

  function arc() {
    var buffer,
        r,
        r0 = +innerRadius.apply(this, arguments),
        r1 = +outerRadius.apply(this, arguments),
        a0 = startAngle.apply(this, arguments) - halfPi$1,
        a1 = endAngle.apply(this, arguments) - halfPi$1,
        da = Math.abs(a1 - a0),
        cw = a1 > a0;

    if (!context) context = buffer = path();

    // Ensure that the outer radius is always larger than the inner radius.
    if (r1 < r0) r = r1, r1 = r0, r0 = r;

    // Is it a point?
    if (!(r1 > epsilon$1)) context.moveTo(0, 0);

    // Or is it a circle or annulus?
    else if (da > tau$2 - epsilon$1) {
      context.moveTo(r1 * Math.cos(a0), r1 * Math.sin(a0));
      context.arc(0, 0, r1, a0, a1, !cw);
      if (r0 > epsilon$1) {
        context.moveTo(r0 * Math.cos(a1), r0 * Math.sin(a1));
        context.arc(0, 0, r0, a1, a0, cw);
      }
    }

    // Or is it a circular or annular sector?
    else {
      var a01 = a0,
          a11 = a1,
          a00 = a0,
          a10 = a1,
          da0 = da,
          da1 = da,
          ap = padAngle.apply(this, arguments) / 2,
          rp = (ap > epsilon$1) && (padRadius ? +padRadius.apply(this, arguments) : Math.sqrt(r0 * r0 + r1 * r1)),
          rc = Math.min(Math.abs(r1 - r0) / 2, +cornerRadius.apply(this, arguments)),
          rc0 = rc,
          rc1 = rc,
          t0,
          t1;

      // Apply padding? Note that since r1 ≥ r0, da1 ≥ da0.
      if (rp > epsilon$1) {
        var p0 = asin(rp / r0 * Math.sin(ap)),
            p1 = asin(rp / r1 * Math.sin(ap));
        if ((da0 -= p0 * 2) > epsilon$1) p0 *= (cw ? 1 : -1), a00 += p0, a10 -= p0;
        else da0 = 0, a00 = a10 = (a0 + a1) / 2;
        if ((da1 -= p1 * 2) > epsilon$1) p1 *= (cw ? 1 : -1), a01 += p1, a11 -= p1;
        else da1 = 0, a01 = a11 = (a0 + a1) / 2;
      }

      var x01 = r1 * Math.cos(a01),
          y01 = r1 * Math.sin(a01),
          x10 = r0 * Math.cos(a10),
          y10 = r0 * Math.sin(a10);

      // Apply rounded corners?
      if (rc > epsilon$1) {
        var x11 = r1 * Math.cos(a11),
            y11 = r1 * Math.sin(a11),
            x00 = r0 * Math.cos(a00),
            y00 = r0 * Math.sin(a00);

        // Restrict the corner radius according to the sector angle.
        if (da < pi$2) {
          var oc = da0 > epsilon$1 ? intersect(x01, y01, x00, y00, x11, y11, x10, y10) : [x10, y10],
              ax = x01 - oc[0],
              ay = y01 - oc[1],
              bx = x11 - oc[0],
              by = y11 - oc[1],
              kc = 1 / Math.sin(Math.acos((ax * bx + ay * by) / (Math.sqrt(ax * ax + ay * ay) * Math.sqrt(bx * bx + by * by))) / 2),
              lc = Math.sqrt(oc[0] * oc[0] + oc[1] * oc[1]);
          rc0 = Math.min(rc, (r0 - lc) / (kc - 1));
          rc1 = Math.min(rc, (r1 - lc) / (kc + 1));
        }
      }

      // Is the sector collapsed to a line?
      if (!(da1 > epsilon$1)) context.moveTo(x01, y01);

      // Does the sector’s outer ring have rounded corners?
      else if (rc1 > epsilon$1) {
        t0 = cornerTangents(x00, y00, x01, y01, r1, rc1, cw);
        t1 = cornerTangents(x11, y11, x10, y10, r1, rc1, cw);

        context.moveTo(t0.cx + t0.x01, t0.cy + t0.y01);

        // Have the corners merged?
        if (rc1 < rc) context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);

        // Otherwise, draw the two corners and the ring.
        else {
          context.arc(t0.cx, t0.cy, rc1, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
          context.arc(0, 0, r1, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
          context.arc(t1.cx, t1.cy, rc1, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
        }
      }

      // Or is the outer ring just a circular arc?
      else context.moveTo(x01, y01), context.arc(0, 0, r1, a01, a11, !cw);

      // Is there no inner ring, and it’s a circular sector?
      // Or perhaps it’s an annular sector collapsed due to padding?
      if (!(r0 > epsilon$1) || !(da0 > epsilon$1)) context.lineTo(x10, y10);

      // Does the sector’s inner ring (or point) have rounded corners?
      else if (rc0 > epsilon$1) {
        t0 = cornerTangents(x10, y10, x11, y11, r0, -rc0, cw);
        t1 = cornerTangents(x01, y01, x00, y00, r0, -rc0, cw);

        context.lineTo(t0.cx + t0.x01, t0.cy + t0.y01);

        // Have the corners merged?
        if (rc0 < rc) context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t1.y01, t1.x01), !cw);

        // Otherwise, draw the two corners and the ring.
        else {
          context.arc(t0.cx, t0.cy, rc0, Math.atan2(t0.y01, t0.x01), Math.atan2(t0.y11, t0.x11), !cw);
          context.arc(0, 0, r0, Math.atan2(t0.cy + t0.y11, t0.cx + t0.x11), Math.atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw);
          context.arc(t1.cx, t1.cy, rc0, Math.atan2(t1.y11, t1.x11), Math.atan2(t1.y01, t1.x01), !cw);
        }
      }

      // Or is the inner ring just a circular arc?
      else context.arc(0, 0, r0, a10, a00, cw);
    }

    context.closePath();

    if (buffer) return context = null, buffer + "" || null;
  }

  arc.centroid = function() {
    var r = (+innerRadius.apply(this, arguments) + +outerRadius.apply(this, arguments)) / 2,
        a = (+startAngle.apply(this, arguments) + +endAngle.apply(this